Mathematical methods and models

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Research in this area is oriented towards the mathematical modelling of a variety of phenomena in science, engineering, business, and industry. Typical applications include quantum and classical fluid dynamics (nonlinear Schrödinger equations, advection-diffusion-reaction equations, nonlinear hyperbolic systems), complex multi-agent systems (kinetic equations, particle methods, multi-scale models), superconductivity and materials science (Ginzburg-Landau equations), evolution of interfaces in physics and biology (minimal surfaces, motion by mean curvature), image processing, mathematical finance (stochastic differential equations, Lévy processes, stochastic control), stochastic models for complex systems, stochastic machine learning, classical and quantum mechanics. This area is characterised by multidisciplinary skills in Analysis of PDEs, Calculus of Variations, Optimal Control, Numerical methods for PDEs, Scientific Computing, Stochastic Analysis, Probability Theory, Mathematical Physics, and Differential Geometry. The research is carried out through collaborations, networks, and projects both at national and international levels. This area can be further divided into sub-areas. Analysis of PDEs and Calculus of Variations: nonlinear partial differential equations, geometric measure theory, optimal transport, variational models in superconductivity theory and materials science, control theory, mean field games. Numerical Analysis and Scientific Computing: numerical methods for hyperbolic systems, Finite Volume and Discontinuous Galerkin schemes, exponential integrators and matrix function approximation, numerical methods for nonlinear Schrodinger equations, numerical methods for kinetic equations, modelling of multi-agent systems. Probability and Mathematical Physics: complex systems, interacting particle systems, stochastic dynamics, mean field games, stochastic partial differential equations, mathematical finance, neural networks and applications, integrable systems, geometric methods in mechanics.
Giacomo Albi
Associate Professor
Sisto Baldo
Associate Professor
Mauro Bonafini
Temporary Assistant Professor
Leonard Peter Bos
Emeritus Professor
Marco Caliari
Full Professor
Giacomo Canevari
Associate Professor
Francesca Collet
Associate Professor
Paolo Dai Pra
Full Professor
Luca Di Persio
Associate Professor
Elena Gaburro
Associate Professor
Antonio Marigonda
Full Professor
Giandomenico Orlandi
Full Professor
Nicola Sansonetto
Associate Professor
Research interests
Topic People Description
Calculus of variations and optimal control; optimization standard compliant  MSC
Existence theories Sisto Baldo
 		Minimal surfaces. Calculus of variations on manifolds.
Hamilton-Jacobi theories, including dynamic programming Antonio Marigonda
 		Nonsmooth Analysis and application to Optmal control. Viscosity solutions of Hamilton-Jacobi equations.
Optimality conditions. Sisto Baldo
 		Asymptotics of variational problems. Variational convergences and Gamma Convergence. Singular perturbations of variational problems.
Variational problems in a geometric measure-theoretic setting Sisto Baldo
 Mauro Bonafini
 Giacomo Canevari
 Antonio Marigonda
 Giandomenico Orlandi
 Nicola Sansonetto
 		Geometric variational and evolution problems: minimal surfaces, motion by mean curvature. Optimal mass transport theory.
Variational principles of physics. Sisto Baldo
 		Variational problems from condensed matter and particle Physics (e.g. Ginzburg-Landau models for superconductivity, Gross-Pitaevskii model for Bose-Einstein condensation, string theory) and their relation with minimal surfaces.
Manifolds standard compliant  MSC
Geometric measure and integration theory, integral and normal currents in optimization Giandomenico Orlandi
 		Geometric measure theory, integral and normal currents; optimization problems for networks of curves and surfaces.
Optimal transportation theory Giandomenico Orlandi
 		Optimal transportation theory
Optimal Transport Antonio Marigonda
 		Analytical and geometrical methods for the study of problems of optimal mass transportation and optimal resource allocation.
Numerical analysis standard compliant  MSC
Approximation of matrix exponential Marco Caliari
 		Polynomial approximation of matrix exponential by interpolation at special nodes.
Numerical approximation Leonard Peter Bos
 Marco Caliari
 		We implement algorithms to calculate a numerical approximation of a complicated function, defined either directly by an explicit formula or procedure or else, for example, defined indirectly as the solution of a differential equation of some type.
Partial differential equations, initial value and time-dependent initial-boundary value problems Giacomo Albi
 Marco Caliari
 Elena Gaburro
 		Solution of non-linear Schrödinger, mean-field and Boltzmann-type equations by pseudo-spectral or meshless methods in space and splitting methods in time.
Ordinary differential equations and applications Giacomo Albi
 		Development of Implicit-Explicit schemes and asymptotic preserving schemes for time dependent problem. Applications in hyperbolic balance laws with diffusive limit and optimal control problems.
Elliptic equations and elliptic systems standard compliant  MSC
Partial differential equations of elliptic type Sisto Baldo
 Giacomo Canevari
 Giandomenico Orlandi
 		Studying existence, regularity, and qualitative properties of solutions to second-order elliptic equations and systems of equations, possibly by variational techniques
Stochastic analysis standard compliant  MSC
Stochastic analysis Luca Di Persio
 		Stochastic analysis, theory of stochastic partial differential equations in finite/infinite dimension, randomly interacting particle systems,with applications to Mathematical Finance.
Large scale interacting random systems Francesca Collet
 Paolo Dai Pra
 		Sistemi di particelle interagenti, limiti macroscopici, giochi a campo medio. Applicazioni alla biologia e alla scienze sociali.
Gruppi di ricerca
Name Description URL
Analysis of PDE and Calculus of Variations Il gruppo si occupa di attività di ricerca nel campo del calcolo delle variazioni, teoria geometrica della misura, teoria del controllo ottimo, teoria del trasporto ottimo, e applicazioni.
Contemporary Applied Mathematics Sviluppo di metodi matematici teorici e computazionali avanzati per fenomeni di trasporto e diffusione in sistemi complessi, l'approssimazione multivariata e problemi di controllo alto dimensionali.
INdAM - Unità di Ricerca dell'Università di Verona Raccogliamo qui le attività scientifiche dell'Unità di Ricerca dell'Istituto Nazionale di alta Matematica INdAM presso l'Università di Verona
Robotica, Intelligenza Artificiale e Controllo Il gruppo di ricerca si occupa di robotica non convenzionale
Projects
Title Managers Sponsors Starting date Duration (months)
HE ERC - Advanced Structure Preserving Lagrangian schemes for novel first order Hyperbolic Models: towards General Relativistic Astrophysics (ALcHyMia) Elena Gaburro UE - Unione Europea 4/1/24 60
Study of the integration of stochastic analysis tools with Machine Learning models in the training and operation of Large Language Models (LLM). Luca Di Persio HPA s.r.l. 2/7/24 11
Data-driven discovery and control of multi-scale interacting artificial agent systems. Giacomo Albi MUR - Ministero dell'Università e della Ricerca 11/30/23 24
Green Inspired Revolution for Optimal-Workforce Management - GIRO-WM Luca Di Persio Fondazione Cassa di Risparmio di Trento e Rovereto 11/1/23 24
Efficient numerical schemes for control problems in nonlinear PDEs and computational social dynamics Giacomo Albi MUR - Ministero dell'Università e della Ricerca 9/28/23 24
Geometric Evolution of Multi Agent Systems Marco Caliari Ricerca di base finanziata dall'Università degli Studi di Verona 11/1/20 24
Controllability and trajectory generation and nonholonomic mechanics Nicola Sansonetto INdAM 7/26/19 12
Geometric aspects in linear and nonlinear potential theory Virginia Agostiniani INdAM 3/11/19 12
PRIN 2017 - Innovative numerical methods for evolutionary partial differential equations and applications Giacomo Albi MUR - Ministero dell'Università e della Ricerca 1/1/19 36
Geometric Measure Theoretical approaches to Optimal Networks Annalisa Massaccesi INdAM 3/22/18 12
Numerical methods for multiscale control problems and applications Giacomo Albi INdAM 2/5/18 12
CUMIN - Currents and Minimizing Networks Giandomenico Orlandi Unione Europea 9/1/17 24
Metodi di controllo ottimo stocastico per l'analisi di problemi di debt-management Antonio Marigonda 3/15/17 12
Geometric evolution of curves, surfaces and networks Giandomenico Orlandi INdAM 3/14/17 12
Stochastic Partial Differential Equations and Stochastic Optimal Control with Applications to Mathematical Finance Luca Di Persio 3/21/16 12
Metodi di viscosità, geometrici e di controllo per modelli diffusivi nonlineari (PRIN 2009 ESTERNO) Antonio Marigonda Ministero dell'Istruzione dell'Università e della Ricerca 7/18/11 24
Fenomeni di propagazione di fronti e problemi di omogeneizzazione (GNAMPA 2010 ESTERNO) Antonio Marigonda INdAM 3/25/10 12
Trasporto ottimo di massa, disuguaglianze geometriche e funzionali e applicazioni (PRIN 2008 ESTERNO) Giandomenico Orlandi Ministero dell'Istruzione dell'Università e della Ricerca 3/22/10 24
Applicazione della teoria del trasporto ottimo alla modellizzazione delle fibre nervose del cervello - Progetto Ricercatori di Recente Afferenza Antonio Marigonda 2/1/10 12
Metodi di viscosità e metrici per l'omogeneizzazione (GNAMPA 2009 ESTERNO) Antonio Marigonda INdAM 3/1/09 12
Energie di interfaccia e problemi parabolici-iperbolici in ambiente discreto e continuo (GNAMPA 2008 ESTERNO) Giandomenico Orlandi INdAM 2/1/08 12
Metodi variazionali nella teoria del trasporto ottimo di massa e nella teoria geometrica della misura (PRIN 2006 ESTERNO) Giandomenico Orlandi Ministero dell'Istruzione dell'Università e della Ricerca 2/9/07 24
Fenomeni di evoluzione non lineari suggeriti dalla Fisica e dalla Biologia (GNAMPA 2006 ESTERNO) Giandomenico Orlandi INdAM 1/1/06 12
Calcolo delle Variazioni (PRIN 2004 ESTERNO) Giandomenico Orlandi Ministero dell'Istruzione dell'Università e della Ricerca 11/30/04 24
Calcolo delle Variazioni (PRIN 2002 ESTERNO) Giandomenico Orlandi Ministero dell'Istruzione dell'Università e della Ricerca 12/16/02 24

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